Answer:
The 95% confidence interval is [tex]10.5 < \mu <13.3[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 41[/tex]
The sample mean is [tex]\= x = 11.9 \ hr[/tex]
The standard deviation is [tex]\sigma = 4.5[/tex]
For a 95% confidence interval the confidence level is 95%
Given that the confidence level is 95% then the level of significance can be mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical values of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
The values is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{ \sqrt{n} }[/tex]
substituting values
[tex]E = 1.96 * \frac{ 4.5 }{ \sqrt{41} }[/tex]
[tex]E = 1.377[/tex]
The 95% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x - E[/tex]
substituting values
[tex]11.9 - 1.377 < \mu <11.9 + 1.377[/tex]
[tex]10.5 < \mu <13.3[/tex]
Find a • b. a = 5i + 7j, b = -4i + 3j
Answer:
[tex]a \cdot b = 1[/tex]
Step-by-step explanation:
[tex] a = 5i + 7j [/tex]
[tex] b = -4i + 3j [/tex]
[tex] a = a_xi + a_yj [/tex]
[tex]b = b_xi + b_yj[/tex]
[tex] a \cdot b = a_xb_x + a_yb_y [/tex]
[tex] a \cdot b = (5)(-4) + (7)(3) [/tex]
[tex] a \cdot b = -20 + 21 [/tex]
[tex]a \cdot b = 1[/tex]
Answer:
[tex]\boxed{-20i^2 -13ij+21j^2}[/tex]
Step-by-step explanation:
[tex]\sf Plug \ in \ the \ values.[/tex]
[tex](5i+7j) \cdot (-4i+3j)[/tex]
[tex]\sf Expand \ brackets.[/tex]
[tex]5i(-4i+3j)+7j(-4i+3j)[/tex]
[tex]-20i^2 +15ij+-28ij +21j^2[/tex]
[tex]\sf Combine \ like \ terms.[/tex]
[tex]-20i^2 -13ij+21j^2[/tex]
Lori wants to buy a radio for 60 dollars.
She can pay $60 now, or she can pay $12
a month for 6 months. How much more will
she pay for the radio if she makes monthly
payments?
Answer:
Lori will pay $12 more if she makes monthly payments
Step-by-step explanation:
to find how much she will pay for 6 months, we have to multiply 12 by 6 to get $72
subtracting the amount she would pay as a down payment
$72 - $60 is $12
Lori will pay $12 more if she makes monthly payments
Do numbers below 0 make sense outside of the context of temperature? If you think so, give some examples to show how they make sense. If you don’t think so, give some examples to show otherwise.
Answer:
Yes, they make sense outside the context of temperature.
Step-by-step explanation:
If you are standing in a line, and mark your current position as 0 then if you take two steps ahead it can be counted as positive and if you take two steps back from your current position it can be counted as negative. The positive and negative can denote your forward and backward movement respectively.
If we denote the growth in companies revenue as positive and dip as negative then it would also make sense. A positive number would mean profit for the company while a negative sign would show loss.
Complete the table using the equation w = m + 4
Answer:
5+4 = 9
6+4 = 10
7+4 =11
Step-by-step explanation:
Answer:
(5,9)
(6,10)
(7,11)
Step-by-step explanation:
w = m + 4
when m = 5,
w = 5 + 4 = 9
when m = 6
w = 6 + 4 = 10
when m = 7
w = 7 + 4 = 11
What is the expression
Answer:
3
Step-by-step explanation:
z - 2x
--------
y
Let x = 3 y = -4 and z =-6
-6 - 2(3)
--------
-4
-6 -6
---------
-4
-12
-----
-4
3
Answer:
3
Step-by-step explanation:
To solve this, we need to plug in each of the numbers to the equation.
x = 3, y = - 4, z = - 6
[tex]\frac{z-2x}{y} = \frac{-6-2(3)}{-4}[/tex]
Let's solve the parenthesis first. - 2 * 3 = - 6.
[tex]\frac{-6-6}{-4}[/tex]
We then subtract -6 - 6.
[tex]\frac{-12}{-4}[/tex]
Then, we divide (cancel out the negatives).
[tex]-12 / -4 =3[/tex]
Our final answer is 3. Hope this helps!
The sum of three numbers is 72 the second number is three times the third the third number is eight more than the first what are the numbers
Answer:
Our three numbers are 8, 48, and 16.
Step-by-step explanation:
Let the first, second, and third numbers be x, y, and z, respectively.
The sum of them is 72. In other words:
[tex]x + y + z = 72[/tex]
The second number y is three times the third number z. So:
[tex]y = 3z[/tex]
And the third number z is eight more than the first number x. So:
[tex]z = x + 8[/tex]
To find the numbers, solve for the system. We can substitute the last two equations into the first:
[tex]x + (3z) + ( x + 8) = 72[/tex]
Substitute again:
[tex]\displaystyle x + 3(x+8) + x+8 = 72[/tex]
Solve for x. Distribute:
[tex]x+3x+24+x+8=72[/tex]
Combine like term:
[tex]5x + 32 = 72[/tex]
Subtract:
[tex]5x = 40[/tex]
And divide:
[tex]x=8[/tex]
Thus, the first number is eight.
And since the third number is eight more than the first, the third number z is 16.
The second number is three times the third. Thus, the second number y is 3(16) or 48.
Our three numbers are 8, 48, and 16.
A square has a side length of 520
meters. What is the perimeter of
the square in kilometers?
Answer: 2.08 km
Step-by-step explanation:
Side of Square = 520 m
Perimeter of Square = Side × 4
= 520 × 4
= 2080 m
1000 m = 1km
2080 m = 2080 ÷ 1000
= 2.08 km
I need help with this please
Answer:
26. 35
27. 65
28. 13
Step-by-step explanation:
26. The big angle POR is given as 59 and the smaller angle inside it (POQ) is given as 24. Since the angles POQ and QOR add up to the angle POR,
QOR = POR - POQ | 59-24 = 35
27. We are given the angles of all the smaller angles in the large angle POS. POQ, QOR and ROS are 19, 31 and 15 respectively. Since all of them add up to create the angle POS, POS = 19+31+15 = 65
28. We can use the second and third given angles (POR and POQ) to find the QOR which we can then use to find ROS. This first step is very similar to 26. We are given POR as 61 and POQ as 28, therefore QOR = 61-28 = 33
Since we now know QOR and QOS, we can repeat the process and deduct that because the two smaller angles add up to the bigger one (QOS), we can find ROS by subtracting QOR (from above) from the given QOS (46):
46 - 33 = 13
Hope this helped!
look at the image for the question?
Answer:
396 in ^3
Step-by-step explanation:
The volume of a rectangular prism is
V = l*w*h where l is the length, w is the width, and h is the height
V = 12 * 3 * 11
V = 396 in ^3
A line is an undefined termi because it
Answer:
Goes on forever.
Step-by-step explanation:
Which of the following inequalities matches the graph?
10
6
-10
Oxs-1
Ox>-1
Oys-1
Oy 2-1
Answer:
y > -1
Step-by-step explanation:
the line is going across the y axis and is everything above -1
help asap!! will get branliest.
Answer:
5/2
Step-by-step explanation:
5^(-3). 2^2.5^6 / (2^3.5^2)
By the law of indices,
=5^(-3+6-2).2^(2-3)
=5^1.2^(-1)
=5. 2^-1
=5/2
If the area of a circle is 16π, the circumference of the circle is:
A. 8π
B. 16π
C. 2π
D. 4π
A gift box shown below is packed with small cubic 1/2 inch blocks. The blocks are packed tightly with no spaces between them.
A. How many blocks are in the gift box?
B. What is the volume of the gift box?
C. Find how much wrapping paper will be needed to wrap the gift box (hint: find surface area).
Step-by-step explanation:
the box is
9 in × 3.5 in × 4.5 in = 141.75 in³
each block is
0.5 in × 0.5 in × 0.5 in = 0.125 in³ (1/8 in³)
so, we can fit
141.75 / 0.125 = 1134
blocks into the box.
and they fit neatly, as the dimensions of the box and the cubes allow a tight packing without any empty left over space in the box.
How would you find the coefficient of the third term in (x+5)^7?
Answer:
The answer is option B
Step-by-step explanation:
To find the coefficient of the third term in
[tex](x + 5)^{7} [/tex]
Rewrite the expansion in the form
[tex](a + x)^{n} [/tex]
where n is the index
So we have
[tex] ({5 + x})^{7} [/tex]
After that we use the formula
[tex]nCr( {a}^{n - r} ) {x}^{r} [/tex]
where r is the term we are looking for
For the third term we are looking for the term containing x²
that's
r + 1 = 3
r = 2
So to find the coefficient of the third term
We have
[tex]7C2[/tex]
Hope this helps you
first of all, the notation is wrong it should be [tex] {}^nC_r \text{ and more usual notation is } {n \choose k} [/tex]
second, the
[tex](r+1)^{\text{th}} \text{ term } T_{r+1} \text{ in the expansion of } (x+a)^n \text{ is } {n \choose r}x^{(n-r)}a^r[/tex]
here [tex] a=5 \text{ and } n=7 \text{ and for } 3^{\text{rd}} \text{ term } T_3, \quad r+1=3 \implies r=2 [/tex]
so the coefficient of third term is, [tex]{7 \choose 2}={7\choose 5}[/tex]
an important property of binomial coefficient you should know:
[tex] {n \choose k}={n \choose {n-k}}[/tex]
and if you interchange [tex] x \text{ and } a[/tex]
only the "order" will get reversed. i.e. the series will start from back.
another thing, the [tex] k^{\text{th}} \text{ term from beginning, is the } (n-k+2)^{\text{th}} \text{ term from behind}[/tex]
Which of the following is equivalent to –2i(6 – 7i)?
Answer:
[tex]\boxed{\sf \bf \ \ -2i(6-7i)=-14-12i \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
[tex]-2i(6-7i)=-12i+14i^2=-14-12i[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
A
Step-by-step explanation:
Answer = A
The time it takes to process phone orders in a small florist/gift shop is normally distributed with a mean of 6 minutes and a standard deviation of 3 minutes. What cutoff value would separate the 2.5% of orders that take the most time to process?
A) 4.76 minutes
B) 3.52 minutes
C) 10.01 minutes
D) 11.00 minutes
E) 12.00 minutes
Laura made $273 for 13 hours of work.
At the same rate, how much would she make for 17 hours of work?
sl
X
$
?
I
as
8
3) The volume of
a wall, 5 times
high as it is board and 8
times as long as it is high, 12.8
(a.metors) Find The Breadth of the
Wall
Answer:
0.4 meters
Step-by-step explanation:
The volume is ...
V = LHB
12.8 m³ = (8(5B))(5B)(B) = 200B³ . . . fill in given values
0.064 m³ = B³ . . . . . simplify
∛0.064 m = B = 0.4 m
The breadth of the wall is 0.4 meters.
Find the area of the shape shown below.
2
2
nd
2
Need help Plz hurry and answer!!!
Answer:
=6 units squared
Step-by-step explanation:
area=1/2h(a+b)
=1/2×2(4+2)
=6
Can u pls help I don’t understand I’ll give u 15 points
Answer: [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
This is a multiplication problem. You are multiplying [tex]\frac{1}{3}[/tex] by 4. This also means 4 divided by 3. They are both the same.
A multiple choice test contains 10 questions with 5 answer choices. What is the probability of correctly answering 5
questions if you guess randomly on each question?
The answer is 1/2 because there are total 10 questions. So, the probability of getting 5 correct answers is 5/10 that is 1/2.
Mark me as brainleist
Jessica just bought a refrigerator for $799. She paid $79.80 in a down payment and will pay the rest in 4 equal installments. How much does she need to pay for each installment?
Answer:
$179.80
Step-by-step explanation:
799-79.80=719. That's the down payment subtracted from the total price of the refrigerator. 719/4, since there's four equal installments, gives you 179.8. Since cents go in 10s, you make it 179.80 and slap a dollar sign in front of that.
Ax + By = C for x. plz sove
Answer:
[tex]\boxed{\boxed{ x=\frac{C-By}{A}; A\neq 0}}[/tex]
Step-by-step explanation:
[tex]Ax+By=C\\\\Ax+By-By=C-By\\\\Ax=C-By\\\\\frac{Ax=C-By}{A}\\\\\boxed{ x=\frac{C-By}{A}; A\neq 0}[/tex]
Hope this helps.
Complete the table for the given rule. Rule: y = x + 3. X ? Y 4. X ? Y 8. X ? Y 5
Answer:
X 1 for Y 4
X 5 for Y 8
X 2 for Y 5
Step-by-step explanation:
We can substitute the values of Y in the formula and then subtract three from both sides.
Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.). lim h → 0 1 + h − 1 h
Answer:
1Step-by-step explanation:
Given the limit of a function [tex]\lim_{h \to 0} \frac{(1+h)-1}{h}[/tex], to evaluate the limit, the following steps must be taken.
Step 1: Substitute h = 0 into the function given.
[tex]= \lim_{h \to 0} \frac{(1+h)-1}{h}\\\\[/tex]
[tex]= \frac{(1+0)-1}{0}\\\\= \frac{1-1}{0} \\\\= \frac{0}{0} (indeterminate)\\[/tex]
Step 2: Apply l'hospital rule
[tex]\lim_{h \to 0} \frac{\frac{d}{dh}[(1+h)-1] } {\frac{d}{dh}(h) } \\\\= \frac{0+1-0}{1}\\ \\= \frac{1}{1} \\ \\= 1[/tex]
Hence the limit of the function [tex]\lim_{h \to 0} \frac{(1+h)-1}{h} \ is \ 1[/tex]
plz someone help me with this question
Answer:
(x+3)^2=-4(y-3)
Step-by-step explanation:
(x-h)^2 = 4p(y-k)
P is the distance between the focus and vertex
P = 1 --> used distance formula for the points of -3,2 -3,3
Vertex is -3,3 --> according to picture
(x+3)^2=-4(y-3)
P is negative since it goes downwards in the picture.
Log 1/10 how do you convert this without a calculator
Answer:
log(1/10) = -1
Step-by-step explanation:
Use the law of exponents and the meaning of logarithm.
1/10 = 10^-1
log(10^x) = x
So, you have ...
log(1/10) = log(10^-1)
log(1/10) = -1
[tex] \frac{3x - 2}{7} - \frac{5x - 8}{4} = \frac{1}{14} [/tex]
Answer:
[tex]x=2[/tex]
Step-by-step explanation:
[tex]\frac{3x-2}{7}-\frac{5x-8}{4}=\frac{1}{14}[/tex]
In order to factor an integer, we need to divide it by the ascending sequence of primes 2, 3, 5.
The number of times that each prime divides the original integer becomes its exponent in the final result.
In here, Prime number 2 to the power of 2 equals 4.
[tex]\frac{3x-2}{7}-\frac{5x-8}{2^{2} }=\frac{1}{14}[/tex]
First, We need to add fractions-
Rule:-
[tex]\frac{A}{B} +\frac{C}{D} =\frac{\frac{LCD}{B}+\frac{LCD}{D}C }{LCD}[/tex]
LCD = [tex]7 \cdot 2^{2}[/tex]
[tex]\frac{4(3x-2)+7(-(5x-8))}{7*2^{2} } =\frac{1}{14}[/tex]
[tex]x=2[/tex]
OAmalOHopeO
Translate the statements into a confidence interval for p. Approximate the level of confidence. In a survey of 8451 U.S. adults, 31.4% said they were taking vitamin E as a supplement. The survey's margin of error is plus or minus 1%.
Answer:
The confidence interval is [tex]0.304 < p < 0.324[/tex]
Step-by-step explanation:
From the question we are told
The sample proportion [tex]\r p = 0.314[/tex]
The margin of error is [tex]E = 0.01[/tex]
The confidence interval for p is mathematically represented as
[tex]\r p - E < p < \r p + E[/tex]
=> [tex]0.314 - 0.01 < p < 0.314 + 0.01[/tex]
=> [tex]0.304 < p < 0.324[/tex]